An automated system for continuous measurements of tracegas fluxes through snow: an evaluation of the gas diffusionmethod at a subalpine forest site, Niwot Ridge, Colorado

Brian Seok Æ Detlev Helmig ÆMark W. Williams Æ Daniel Liptzin ÆKurt Chowanski Æ Jacques Hueber

Received: 18 September 2008 / Accepted: 24 February 2009 / Published online: 6 May 2009

� The Author(s) 2009. This article is published with open access at Springerlink.com

Abstract An experimental system for sampling

trace gas fluxes through seasonal snowpack was

deployed at a subalpine site near treeline at Niwot

Ridge, Colorado. The sampling manifold was in place

throughout the entire snow-covered season for

continuous air sampling with minimal disturbance

to the snowpack. A series of gases (carbon dioxide,

water vapor, nitrous oxide, nitric oxide, ozone,

volatile organic compounds) was determined in

interstitial air withdrawn at eight heights in and

above the snowpack at *hourly intervals. In thispaper, carbon dioxide data from 2007 were used for

evaluation of this technique. Ancillary data recorded

inlcuded snow physical properties, i.e., temperature,

pressure, and density. Various vertical concentration

gradients were determined from the multiple height

measurements, which allowed calculation of vertical

gas fluxes through the snowpack using Fick’s 1st law

of diffusion. Comparison of flux results obtained

from different height inlet combinations show that

under most conditions fluxes derived from individual

gradient intervals agree with the overall median of all

data within a factor of 1.5. Winds were found to

significantly influence gas concentration and gradi-

ents in the snowpack. Under the highest observed

wind conditions, concentration gradients and calcu-

lated fluxes dropped to as low as 13% of non-wind

conditions. Measured differential pressure amplitude

exhibited a linear relationship with wind speed. This

suggests that wind speed is a sound proxy for

assessing advection transport in the snow. Neglecting

the wind-pumping effect resulted in considerable

underestimation of gas fluxes. An analysis of depen-

dency of fluxes on wind speeds during a 3-week

period in mid-winter determined that over this period

actual gas fluxes were most likely 57% higher than

Electronic supplementary material The online version ofthis article (doi:10.1007/s10533-009-9302-3) containssupplementary material, which is available to authorized users.

B. Seok � D. Helmig � M. W. Williams �D. Liptzin � K. Chowanski � J. HueberInstitute of Arctic and Alpine Research (INSTAAR),

University of Colorado at Boulder, Boulder,

CO 80309-0450, USA

B. Seok (&)Department of Atmospheric and Oceanic Sciences,

University of Colorado at Boulder, Boulder,

CO 80309-0311, USA

e-mail: seok@colorado.edu

M. W. Williams

Department of Geography, University of Colorado at

Boulder, Boulder, CO 80309-0260, USA

D. Liptzin

Department of Ecology and Evolutionary Biology,

University of Colorado at Boulder, Boulder,

CO 80309-0334, USA

Present Address:D. Liptzin

Department of Environmental Science, Policy, and

Management, University of California at Berkeley,

Berkeley, CA 94720-3114, USA

123

Biogeochemistry (2009) 95:95–113

DOI 10.1007/s10533-009-9302-3

http://dx.doi.org/10.1007/s10533-009-9302-3

fluxes calculated by the diffusion method, which

omits the wind pumping dependency.

Keywords Diffusion model � CO2 flux �Gradient method � Snowpack � Wind-pumping

Introduction

Recent research in snow-covered temperate, alpine,

and arctic environments shows that subniveal (under

the snow) soil respiration can result in substantial

fluxes of carbon dioxide (CO2) through the snowpack

(Sommerfeld et al. 1993; Brooks et al. 1996; Zimov

et al. 1996; Oechel et al. 1997; Mariko et al. 2000;

McDowell et al. 2000; Welker et al. 2000; Roehm and

Roulet 2003; Monson et al. 2005, 2006). The winter-

time CO2 flux through the snow can contribute in

excess of 20% to the annual carbon budget (Winston

et al. 1997). To date, studies of trace gas flux through

snow have focused primarily on CO2. These findings

suggest that microbial processes in underlying soil

similarly may drive the flux of other gases such as nitric

oxide (NO), nitrous oxide (N2O), and methane (CH4).

Therefore, these processes warrant consideration in the

annual ecosystem carbon (C) and nitrogen (N) budgets

of seasonally snow-covered ecosystems (Sommerfeld

et al. 1993; Brooks et al. 1996; VanBochove et al.

1996; Mast et al. 1998; Yashiro et al. 2006).

The ecological controls on the trace gas fluxes

through the seasonal snowpack are still poorly

known, in part because of the difficulty in measuring

these fluxes and their dependencies during the winter

season. The trace gases CO2, CH4, and N2O are

greenhouse gases that play important roles in climate

forcing. NO is a precursor of tropospheric ozone

(O3), which is also a greenhouse gas, formed by

photochemical reactions. Several studies have

pointed out the high sensitivity of respiration, deni-

trification, and other processes, which produce these

gases, to soil temperature under the seasonal snow-

pack. In turn, the soil temperature tends to increase

with increasing snow depth because the insulating

quality of snow cover increases with depth (Brooks

and Williams 1999). Consequently, the depth and

duration of the seasonal snowpack have been shown

to have notable impacts on trace gas exchanges and

ecosystem C and N budgets (Williams et al. 1998;

Monson et al. 2006). For these reasons, there is a

need to better quantify these processes, their behav-

ior, and dependency on conditions such as snowpack

properties, snow chemical composition, and soil

biogeochemistry, in order to develop conceptual

models for the description of these trace gas fluxes

under current and future climate conditions.

We have improved experimental protocols for the

measurement of fluxes of trace gases through a

seasonal snowpack over five winter seasons (2004–

2008) at a high elevation subalpine site in the

Colorado Rocky Mountains. Trace gases studied

included CO2, nitrogen oxides (NOx = NO ? NO2),

N2O, O3, and volatile organic compounds (VOC).

The high resolution, multiple season data obtained

were used to test the gas diffusion model (DM)

method for deriving quantitative C and N winter

balances. The DM approach has been the most

common method for evaluating trace gas flux through

snow (McDowell et al. 2000), as it has a number of

advantages over other flux techniques such as cham-

ber methods and eddy covariance measurements. In

particular, the concentrations and gradients of trace

gases in the seasonal snowpack are often substantially

higher than ambient levels. This allows for more

robust measurements and experiments appropriate for

complex mountainous terrain and wintertime condi-

tions. Furthermore, these snowpack gradient mea-

surements can be conducted without meeting the

stringent requirements for homogenous and flat

terrain essential for eddy covariance measurements.

The DM relies on the assumption that gas transfer

inside the snowpack is determined by molecular

diffusion. However, there are other factors such as

pressure-related phenomena that influence gas

exchange from the soil through any permeable

medium (in particular, snow) to the atmosphere

(Massman 2006). A number of studies (Massman

et al. 1997; Jones et al. 1999; Hubbard et al. 2005;

Takagi et al. 2005; Suzuki et al. 2006) pointed out the

large potential error that may occur when the DM

approach is applied to trace gas flux through the

snowpack because of the effects of advection or

wind-pumping. However, quantitative descriptions

and corrections of this effect on the flux calculation

remain highly uncertain.

In this paper, we present the experimental

approach that we have developed over the last

5 years for all winter measurements of trace gas

fluxes through a seasonal snowpack. Here, we focus

96 Biogeochemistry (2009) 95:95–113

123

on the flux of CO2 during 2007, but believe that this

evaluation is applicable to other trace gases and other

years. The decision to use CO2 for evaluating our

trace gas sampling system was because the CO2record has been the longest and most complete of all

gases studied to date, the relative precision and

accuracy of its analytical measurement was highest,

thus minimizing errors from the analytical determi-

nation, and the CO2 data offered the highest number

of comparison with studies reported in the literature.

We evaluated potential errors in the estimation of

CO2 fluxes through snow including sampling fre-

quency, number of measurement heights within the

snowpack, and physical properties of the snowpack

such as the density of snow. Errors associated with

the DM technique will be discussed with particular

emphasis on the influence of wind-pumping. Results

and discussion of measured gas fluxes and its

ecological significance can be found in papers by

Filippa et al. (2009, for N2O), Helmig et al. (2009, for

NOx), and Liptzin et al. (2009, for CO2).

Diffusion model (DM) measurement technique

The DM method appeared to be most suitable for this

study, because it allowed continuous long-term mea-

surements throughout the winter season with relatively

simple measurement techniques. This method pro-

vided a direct approach to measuring the gas transport

through the snowpack, since trace gases were sampled

from inside the snow. In past research, gases from the

snowpack were typically drawn from two levels,

the soil–snow interface and the atmosphere above the

snow surface, to obtain a concentration gradient (e.g.

Jones et al. 1999; Takagi et al. 2005; Monson et al.

2006; Suzuki et al. 2006). Besides the measurement of

trace gases at different heights, the DM method

depends on the physical properties of the porous

medium. For the snowpack, this involves measure-

ments of snow depth, density, and temperature. A

newer technique not evaluated here involves measure-

ments of gas concentration in the snowpack using

nondispersive infrared (NDIR) sensors (Takagi et al.

2005).

The DM method is based on Fick’s 1st law of

diffusion. The underlying theory assumes that the

transport of a gas, e.g., CO2, in the snowpack operates

primarily in the vertical dimension with fluxes dictated

by the concentration differential. Within the horizontal

footprint of the CO2 measurement, snow properties are

assumed constant in each arbitrary layer of the

snowpack, leading to consistent CO2 concentrations

at each layer in the snowpack. Thus, CO2 efflux

through the snowpack is calculated using the equation

FCO2 ¼ �DCO2oCCO2

oz

� �; ð1Þ

where FCO2 is the molecular flux of CO2(lmol m-2 s-1), DCO2 is the diffusivity of CO2 inthe snowpack airspace at the qz interval (mol m2 s-1),and oCCO2=oz is the CO2 concentration gradient in the

snowpack (lmol m-3). Therefore, the flux of gas isdirectly proportional to the concentration gradient.

This indicates that any changes in the concentration

gradient term will directly change the flux. The

diffusivity DCO2 can be estimated using the relation

DCO2 ¼ /sDP0P

T

T0

� �a; ð2Þ

where / is the snowpack porosity, s is the tortuositycoefficient, D is the diffusion coefficient of the specific

gas under consideration at standard temperature and

pressure (T0 = 273.15 K and P0 = 1,013 hPa), i.e.,

D = 0.1381 9 10-4 m2 s-1 for CO2. P is the ambient

pressure (hPa), T is the snowpack temperature (K), and

the exponent a = 1.81 is a theoretically set coefficientexplained by Massman (1998). Snowpack porosity /is calculated by

/ ¼ 1� qsnow=qiceð Þ; ð3Þ

where qsnow is the measured density of snow at the qzinterval (kg m-3), and qice is the density of ice(917 kg m-3, Eisenberg and Kauzmann 1969). For

the tortuosity constant s, Duplessis and Masliyah(1991) developed a theoretical relationship where the

tortuosity can be derived from the porosity as

s ¼ 1� 1� /ð Þ2=3

/: ð4Þ

However, we used

s ¼ /1=3; ð5Þ

which is a relationship that was empirically devel-

oped from a snowpack in similar regions as our study

site (Mast et al. 1998; Hubbard et al. 2005). Some

researchers dealt with tortuosity by either ignoring it

or by letting it be equal to 1 (e.g. Sommerfeld et al.

Biogeochemistry (2009) 95:95–113 97

123

1993), or compensating for its effects by reducing the

calculated flux value by 35% (e.g. Fahnestock et al.

1998).

Materials and methods

Study site

This study was conducted at the Soddie site on Niwot

Ridge in an open meadow surrounded by ribbon forest

just below tree line near the Continental Divide

in the Colorado Rocky Mountains (40�0205200N;105�3401500W; 3,345 m above sea level). The site ison a 10� southwest facing slope (Erickson 2004). It hasan underground laboratory 3 9 9 9 2.4 m in size, line

power, and an array of snow and zero-tension soil

lysimeters (Williams et al. 2009). The soil in the open

meadow is classified as a mixed Typic Humicryept

(Soil Survey Staff 2006) and the forest vegetation is

primarily a mixture of spruce (Picea englemannii) and

fir (Abies lasiocarpa) [Williams et al. 2009]. The depth

of A horizon is *34 cm; soil composition is 46%sand, 33% silt, 21% clay, and 31% organic matter in

the upper 10 cm. The soil pH ranges between 4.7 and

5.0 (Seastedt 2001).

Trace gas sampling system

Snowpack gas flux studies began in the 2003–2004

winter season and have continued with additional gas

and physical snowpack measurements. The introduc-

tion paper in this issue by Williams et al. (2009)

provides the history of the studies. In this manuscript,

we report the system configuration from the 2006–

2007 winter season (from here on referred to as

winter 2007), because this season has the most

extensive measurements to date. The photographs in

Fig. 1 and the schematic in Fig. 2 depict the multi-

inlet snow tower used in winter 2007. The snow

tower was constructed of square aluminum alloy

(3.8 9 3.8 cm) tubing with 60 cm long cross bars

(1.3 9 1.3 cm) at heights of 0, 10, 30, 60, 90, 120,

150, and 245 cm above the ground. The tower was

installed in fall 2006, and snow was allowed to

accumulate around it. The snowpack surrounding the

tower was not disturbed throughout the winter season.

Each of the eight cross bars supported a pair

of sampling inlets. The inlets were fitted with

25 mm Acrodisc� hydrophobic polytetrafluoroethyl-

ene (PTFE) syringe filters (Pall Life Sciences, Ann

Arbor, Michigan, USA) to prevent debris from

entering the sampling line. Air was drawn at a rate

of 1.5–3 L min-1 from each sampling height depend-

ing on the number of chemical measurements con-

ducted. Since the sampling flow was split between the

paired inlets, the effective sampling rate per inlet was

0.75–1.5 L min-1.

The selection of a pair of inlets for sampling at a

particular height on the tower was done through an

array of eight solenoid valves. Sampling through each

pair of inlets was done sequentially from the 245 cm

height to the 0 cm height. Each sampling interval was

10 min long, with trace gas contents determined in

this gas flow every 10 s. From that record, 1-min

averages were calculated for each trace gas, sampling

interval, and measurement height. During the transi-

tion from one sampling height to the next, concen-

tration readings for both gases adjusted over *1 minto the new level at the lower inlet. A complete cycle

took 80 min, and there were 18 cycles per day. The

manifold used 2-way solenoid valves with PTFE

body seals (Cole-Parmer, Vernon Hills, Illinois,

USA). All the sampling lines and valves were

conditioned over night with a flow of 2–3 L min-1

of air containing 200–300 ppb ozone prior to instal-

lation to minimize the loss of O3 in the manifold

during subsequent field sampling. All sampling tubes

were directed to the underground laboratory, which

housed the analytical instruments. Sampling lines

were all perfluoroalkoxy (PFA) Teflon�, inner diam-

eter of 3.9 mm and outer diameter of 6.4 mm (Parker

Hannifin, Cleveland, Ohio, USA), with equal lengths

of 18 m. Sections of the sampling lines outside the

laboratory were wrapped in pipe insulation with a

self-controlling water pipe heater to maintain line

temperatures slightly above 0�C. This was done toprevent water from freezing and clogging the sam-

pling lines.

Monitored gases included CO2, H2O, NOx, N2O,

and O3. CO2 and H2O were measured using a LI-7000

IRGA (LI-COR Environmental, Lincoln, Nebraska,

USA). NOx and O3 were measured using a model

42CTL chemiluminescence NOx analyzer, and model

49 UV photometric O3 analyzer, respectively (Thermo

Environmental Instruments, Franklin, Massachusetts,

USA). N2O was measured by isothermal gas chroma-

tography with electron capture detection (GC-ECD)

98 Biogeochemistry (2009) 95:95–113

123

[Shimadzu GC-8AIE, Shimadzu Scientific Instru-

ments, Columbia, Maryland, USA]. On site instrument

calibrations for the LI-7000 IRGA, the model 42CTL

chemiluminescence NOx analyzer, and the Shimadzu

GC-8AIE were automated. More details on these

analytical measurements and calibration procedures

are presented elsewhere (Filippa et al. 2009, for the

GC-8AIE; Helmig et al. 2009, for the 42CTL; Liptzin

et al. 2009, for the LI-7000 IRGA). The sampling

manifold, calibration system, and data acquisition

were controlled through an array of digital input/

output modules, temperature input components, and

LabVIEW software (National Instruments, Austin,

Texas, USA). The GC-ECD signals were acquired

through a PeakSimple system (SRI Instruments,

Torrance, California, USA).

Ancillary data

Temperatures at each sampling height were measured

using type-E thermocouples (Omega Engineering,

Inc., Stamford, Connecticut, USA) that were covered

by white shrink tubing to reduce radiation artifacts.

Wind speed, at 6 m above the ground on a

meteorological (MET) tower 10 m away, was mea-

sured using a 05103-L R.M. Young Wind Monitor

(Campbell Scientific, Logan, Utah, USA). Barometric

pressure was measured using a CS105 Vaisala

PTB101B Barometer (Campbell Scientific, Logan,

Utah, USA). Differential pressure between the soil–

snow and snow–atmosphere interfaces was collected

at the MET tower using a differential pressure sensor

(PX277-0.1D5V, Omega Engineering, Inc., Stam-

ford, Connecticut, USA) with 1 Hz sampling rate and

1-min averages stored. The high pressure inlet was

placed at 3 m above the soil surface and the low

pressure inlet was placed on the ground. Given this

setup, if pressure at the ground was greater than at the

snow surface, then the resulting pressure gradient was

measured as a negative signal.

Readings of snow depth were conducted at

1–2 week intervals from calibrated marks on the

snow tower. Gaps in the snow depth record were

filled by comparing and interpolating the daily snow

depth record from the SNOTEL site, 1.5 km from the

Soddie. An analysis of the linear correlation between

concurrent snow-depth data from these two sites

resulted in a r2 = 0.91. These snow depth data were

Fig. 1 Series ofphotographs showing the

snowpack sampling tower

(snow tower). The left

picture was taken before the

onset of snowfall in autumn

2006. The upper-rightpicture shows the snow

tower buried in *2 m ofsnow with the top sampling

inlet (at 245 cm) above the

snowpack on 11 March

2007. The lower-right photoshows the syringe fiber

glass filter and the type-E

thermocouple mounted to

one of the ends of the

horizontal cross arms on the

snow tower

Biogeochemistry (2009) 95:95–113 99

123

used for flux calculations including the ambient air

measurement data (245 cm). An effective snowpack

diffusion distance to the snow surface was deter-

mined by calculating the distance from the respective,

fixed height inlet pair to this determined snow surface

height. Gas measurements from the 245 cm height

were assumed to be representative for conditions at

the snow-atmosphere interface. This simplification

neglects the concentration gradients between the

snow surface and the 245 cm height.

Soil moisture was measured using four CS616-L

Water Content Reflectometers with 30 cm long

probes installed vertically into the soil in a 1 m

radius from the snow tower (Campbell Scientific,

Logan, Utah, USA), following the protocol at the C-1

Ameriflux site on Niwot Ridge (Bowling et al. 2009),

Fig. 2 Schematics of winter 2007 season snowpack samplingtower with plumbing and instrument configuration. The sky-blue dotted pattern area is the snowpack. The brown dashedline defines the ground. The instruments are located in anunderground lab. Abbreviations of the cylinder labels in the

diagram reflect the following: BA = breathing air standard,

C = 1% CO2 standard, N1 = 320 ppb N2O standard,

N2 = 408 ppb N2O standard, N3 = 485 ppb N2O standard,

NO = 100 ppb NO standard, P5 = 5% CH4/95% Ar carrier

gas (Color figure online)

100 Biogeochemistry (2009) 95:95–113

123

with the average of the four sensors used for all

further data applications.

Snow density was measured in an adjacent open

meadow area*30 m away from the primary study sitewith similar vegetation and slope characteristics.

Snow pits were dug every 1–2 weeks, upslope first

and progressed downhill for each new snow pit. Snow

properties including depth, density, grain type, grain

size, and stratigraphy were measured using previously

published protocols (Williams et al. 1996, 1999).

Results

Snow physical properties

Continuous snowpack at this site typically develops

between the end of October and early November. The

seasonal snow cover reached a maximum depth of

2.2 m in March 2007, and all snow had melted by the

first week of June (Fig. 3). The snowpack develop-

ment in 2007 was similar to our five seasons of

measurements, where seasonal maximum snowpack

depths of 1.8–2.2 m occurred between day of year

(DOY) 65 and 85. While there were occasional minor

reductions in snowpack depth throughout the winter,

with a more significant one occurring during DOY

80–85 in 2007, the springtime snow melt with

significant and continuous snow depth reductions

did not commence until DOY 130. The physical

changes associated with this transition are also

evident in the temperature and density records.

Snowpack temperatures were usually warmer than

ambient air temperatures throughout the season

(Fig. 3a). The average air temperature during the

snow-covered period was -5.2�C, with minimumvalues of -25�C in mid-winter and an increasingtrend in late winter and early spring. The diurnal and

daily fluctuations of air temperature progressively

damped within the first 10–50 cm below the snow

surface. The temperature at the soil–snow interface

increased to about 0�C when the snowpack reached adepth of *12 cm and remained as such until the endof the season (Fig. 3a). At DOY 67, the upper

snowpack layers suddenly warmed. The entire snow-

pack turned isothermal over an 8 day period. How-

ever, it took another 55 days from that point until

significant snow melt occurred.

Snowpack density generally increased over time

(Fig. 3b). The initial density was *200 kg m-3 early

Fig. 3 a A temporal and vertical development of thesnowpack temperature. The black solid line is the snow heightabove the ground (cm). The color bar is the snowpacktemperature (�C). The inverted dark grey triangles denote timewhen actual snow depth measurements were taken. The gaps in

the snow depth data were filled through extrapolating daily

snow depth measurements from the nearby SNOTEL site (see

text for details). b Contour plot of snow density (kg m-3)generated from the biweekly snow pit excavation with 10-cm

vertical resolution. The inverted green triangles denote thedates when actual snow density samples were taken. Gaps

between sampling periods were filled through linear interpo-

lation (Color figure online)

Biogeochemistry (2009) 95:95–113 101

123

in the season; the maximum density measured of

500 kg m-3 occurred during the snowmelt period.

Density normally increased with depth due to com-

pression caused by the overlying snow. However, at

depths below 60 cm, density remained lower and

showed little change over time until active snowmelt.

This section of the snowpack was composed of kinetic

grains (depth hoar), which resists compression.

CO2 and H2O vapor concentrations within the

snowpack

A typical plot of the snowpack concentrations of CO2and H2O vapor during a sampling cycle is presented

in Fig. 4. After 3 min of the transition between

levels, concentrations of CO2 and H2O vapor

remained relatively constant for the remainder of

the measurement interval. Because of the changing

signal during the transition from one inlet to the next,

the five points around the transition period were

omitted for calculating the gas concentration for each

measurement time interval (Fig. 4).

CO2 fluxes

The time series of calculated daily mean fluxes from

all possible gradient combinations for winter 2007 is

shown in Fig. 5. These data show a remarkable

variability both between results from different inlet

heights and between measurement days. Figure 5 also

shows the median value calculated from all available

gradient interval fluxes at a given time. Closer

inspection of this record revealed that individual

gradient data typically fall within a range of ±50%

of the overall median, but it was not uncommon that

data from a selected gradient deviated up to 100%

from the median. Results derived from measurements

at the 0 cm inlet frequently deviated from the other

inlet data, with gradients between the 0 and 10 cm

inlets often being unusually small and on occasion

even negative. This behavior was interpreted as this

measurement interval being too close to the ground

and within the surface roughness layer at this site,

where consistent gradients are not well developed.

Figure 5 also shows the median value calculated from

Fig. 4 Example of a timeseries of CO2 and H2O

vapor concentration data

during one sampling cycle

on 11 March 2007 with the

x-axis scale indicating timefrom the beginning of the

cycle (2:40 am). The dotsare 1-min averages of data

collected every 10 s. The

white dots in each 10-minsampling interval represent

the data that were averaged

for determining gas

concentration gradients

(qC/qz). The black dotswere omitted from the

calculation for determining

the gas concentration

gradient because the values

may be compromised

during the switching

between sampling inlets.

The snowpack depth during

this sampling cycle was

1.87 m

102 Biogeochemistry (2009) 95:95–113

123

all available gradient interval fluxes at a given time.

Our estimate of the diffusive CO2 flux based on the

seasonal average of the daily mean ranged from 0.58 to

1.08 lmol m-2 s-1 in 2007, depending on the pairs ofinlets used for the gradient calculation (Fig. 5).

However, of the 27 gradient combinations, sixteen

of them gave results between 0.70 and 0.90 lmolm-2 s-1. The linear correlation of the all-season data

from the 27 gradient combinations illustrated that—

not unexpectedly—correlations were highest where

gradient intervals overlap due to the autocorrelation in

these data. For example, the correlation coefficient for

gradients calculated from 90 to 60 cm and from 120 to

30 cm was 0.99. Furthermore, correlations were high

for data from adjacent gradients (please see Fig. 4 in

Filippa et al. (2009), which graphically displays the

corresponding analysis for calculated N2O fluxes from

the 90–60 cm vs. the 60–30 cm gradient data), and

became weaker the further the gradients were sepa-

rated vertically. Also, better agreement was generally

seen in data from the middle of the snowpack, whereas

results from sampling near the bottom and involving

measurements from the ambient inlet often showed

weaker correlations. The correlation coefficient r was

only 0.29 between gradients calculated from 30 to

10 cm and from 120 to 90 cm. In essence, the linear

correlation results of the fluxes were dictated by the

concentration gradient, as shown in Eq. (1). Absolute

correlation values r of 1 or close to 1 between

different-height gradients implied that the fluxes

through the snowpack were constant, which is a key

assumption of the DM. This behavior also implies that

diffusion was the dominant process in the transport of

CO2 though the snowpack. Our multiple-inlet gradient

and flux data illustrate that for the center portion of the

snowpack, these conditions (i.e., linear concentration

gradients and dominant diffusion transport) were

reasonably well met and that the diffusion model

was an appropriate tool for estimating fluxes. Conse-

quently, most of our subsequent analyzes were done

using the data from the 60–30 cm gradient interval.

These data showed relatively high correlation with

most non-overlapping inlet pair combination (range in

r values of 0.29–0.80). Furthermore, the 60–30 cm

inlet data were the longest and most steady record for

the 2005–2006 winter season (here on as winter 2006)

and winter 2007.

Discussion

Potential sampling effects

Active sampling from interstitial air in the snowpack

represents a disturbance to the natural air transport and

this can generate artifacts in the measured snowpack

data (Albert et al. 2002; Domine et al. 2008). We

evaluated the potential artifact caused by our sampling

Fig. 5 Daily winter 2007CO2 flux for all sampling

height combination. The

thick black line depicts thedaily median flux data

calculated from the results

of all gradient combinations

(Color figure online)

Biogeochemistry (2009) 95:95–113 103

123

technique using an approach similar to the one

presented by Bowling et al. (2009). Our sampling

system pulled *20 L of air from the paired inletsduring each sampling interval. The *10 L of airwithdrawn at each inlet, at a snowpack density of

400 kg m-3 (which was the seasonal average), and

assuming a sphere volume, would yield an effective

radius of *16 cm per inlet of the sampling volume.All, but one, sampling ports were 30 cm apart in the

vertical, so there is very little overlap within this

radius. (The closer distance between the 0 and 10 cm

height inlet pairs was the only exception to this

requirement). Based on gas-phase diffusive transport

only (Seinfeld and Pandis 2006, p 551), we estimated

that it would take *44 min within this volume for airto re-equilibrate to its original condition. This is faster

than the 80-min cycle used in our experiment. [With

increased (decreased) snow density, the re-equilibrium

time would increase (decrease), and the sample will

reflect a larger (smaller) volume of snowpack]. Data

from our sampling protocol confirmed the validity of

these assumptions. As seen in Fig. 4, other than during

the transition period, there was comparatively little

change in gas concentrations during the 10-min

sampling interval. This meant that gas sampled during

this time remained relatively representative of the

given inlet height. Also, closer inspection of these

records revealed that the relative change of signal was

largest for the 0 cm measurement height, which

reflects the fact that the available airspace extends

only in one direction; therefore, air that replaced the

sampled air volume is expected to be drawn from a

larger vertical distance. The larger degree of overlap-

ping sampling volumes for the 0 and 10 cm heights

explained to some extend the deviating behavior in

observed gradient from these two heights. In summary,

our results were in agreement with the findings of

Bowling et al. (2009) who re-measured several inlets

25 min after the initial measurement and found no

difference in CO2 concentrations or isotopes of carbon

and concluded that the advective influence of their

sampling under these conditions was negligible.

Dependence of CO2 flux on environmental

conditions

In general, CO2 fluxes gradually increased over the

snow-covered season, reaching a maximum around the

onset of snowmelt. An interesting question was what

drove the daily variations in CO2 (Fig. 5), and if the

change in flux was driven by changes in the source

term, i.e., day-to-day changes in the emission of CO2from soil to the snowpack, or to other physical or

chemical processes that influenced the flux calculation.

For the investigation of this question, we focused on

the 30-day time period between DOY -11 and 19 when

the snow depth was relatively constant at *120 cm(Fig. 6a). Over this time span, the soil volumetric

water content remained constant at *0.20 m3 m-3

(Fig. 6b), and the temperature near the soil–snow

interface was always*0�C (Fig. 6d). In contrast to therelatively constant snow depth, snow temperature, and

soil moisture content, data for wind speed ranged over

more than an order of magnitude from\0.2 to 6 m s-1

(Fig. 6c). In turn, there was a tendency that higher

wind speeds were associated with lower differential

pressures (Fig. 6c). Concentrations of CO2 increased

from ambient levels at the snow surface (* 385 ppm)to *4,000 ppm at the bottom of the snowpack(Fig. 6e). Comparison between the CO2 concentration

and wind speed time series data suggested that CO2concentrations in the snowpack generally decreased

with increasing wind speed. For example, between

DOY -6 and -5, at the 10 cm level, CO2 concentrations

decreased by almost a factor of 2 from 2,690 to

1,475 ppm, as wind speed increased from 1.5 to

5.9 m s-1. As a result, calculated CO2 fluxes

decreased from 0.67 to 0.16 lmol m-2 s-1 (Fig. 6f).

Uncertainties in flux estimates using the diffusion

model

Snow permeability and gas transport are related to

snow density (Albert and Hardy 1995; Albert and

Shultz 2002; Albert et al. 2004) as permeability is

affected by porosity and tortuosity, even though there

is no direct relationship between porosity, tortuosity,

and permeability (Hardy et al. 1995). In our flux

calculation, gas diffusivity, following Eq. (2), was

derived indirectly from snow density, as porosity and

tortuosity were calculated from the density values

[see Eqs. (3) and (5)]. For example, the diffusion rate

at a density of 250 kg m-3 was 87% faster than at a

density of 500 kg m-3, assuming all other variables

were unchanged. Thus, errors in the estimate of CO2flux through snow caused by incorrect measurements

of density varied as density changed. Errors in

measuring the density of snow have been estimated

104 Biogeochemistry (2009) 95:95–113

123

at 10–15% (Sommerfeld et al. 1996; Hubbard et al.

2005). In our case, the uncertainty in applied density

was likely higher, as we applied density data from an

adjacent plot, and the biweekly density determina-

tions did not allow for capturing density changes that

occurred at higher frequency than this sampling

interval. We evaluated how errors in measuring

density propagated to errors in estimating the flux

of CO2 using errors in the measurement of density of

±10, 20, and 30%. The calculated error increased

non-linearly at higher snow densities and with the

uncertainty in the determination of snow density. For

instance, a 10% error in the measurement of snow

density resulted in an error in the estimated CO2 flux

on the order 5% for a snow density of 300 kg m-3

but more than 10% at a density of 500 kg m-3. For

the range of snow densities encountered during the

experiment at the Soddie sites, we estimated that the

error in calculating the flux of CO2 ranged from 2 to

9% (Supplementary Material, Fig. S1). Another

potential complication in the diffusion flux calcula-

tion was the presence of crust and ice layers, which

may constitute diffusion barriers that were not

considered in the Fick’s law calculation. Snow pit

analyses showed that ice layers were uncommon at

the site, as snow surface temperatures at this high

elevation generally remain below freezing (which

avoids freeze-thaw events that form crust and ice

layers) until the onset of the spring melt period. There

are several reasons why our sampling technique is

rather robust against the influence of inhomogeneous

snow density, and ice lenses and crusts. The variation

Fig. 6 Dataset from DOY-11 to 19. a Snow heightfrom the ground. The greydots are the actual snowdepth measurements. The

solid line is the interpolateddata based on the daily

SNOTEL snow depth

measurements (see text for

details). b Soil moisturedata. The line is the averageof the four soil moisture

sensors surrounding the

snow tower in a 1-m radius.

c Wind speed (dark bluesolid line) and differentialpressure (sky-blue solidline). d Temperature datafrom the snow tower (in and

above the snowpack). e CO2concentration in and above

the snowpack measured

from the snow tower. The

green and red arrows markthe start and end when the

instrument range was

maxed out at 3000 ppm at

one or more sampling

heights. f Calculated fluxusing the 30 and 60 cm inlet

data without consideration

of wind correction (Color

figure online)

Biogeochemistry (2009) 95:95–113 105

123

of snowpack density was accounted for in the flux

calculation. For each sampling interval, the snowpack

density corresponding to that sampling interval and

snowpack layer was used to calculate the fluxes. This

resolves the temporal and spatial variations the

snowpack density would have on the flux. Concep-

tually, our sampling system in the snowpack was

similar to a chamber with open sides giving it

horizontally infinite spatial scale. Since ice lenses and

crusts do not span over an infinitely large area, gases

diffusing through the snowpack would continue to

travel around the ice lenses and crusts, and gas

concentration at each arbitrary horizontal layer in the

snowpack would equilibrate and maintain a distinct

concentration gradient. The deviation in flux results

from different height intervals affirms (Fig. 5) and

defines the maximum effect that this error; as already

elucidated above, these data show that flux results

generally agreed within a factor of 1.5 from different

height intervals.

Errors in the measurement of the snowpack height

and the height of the tower arms were also a source of

uncertainty when calculating the flux of CO2. All

gradient distances within the snowpack were deter-

mined by the distance between the tower cross arms.

Due to the pressure exhibited from the compacting

and creeping snow, some of the cross arms were bent

by up to 5 cm, which introduces an error of as much

as 15% in the flux calculation. The flux from any inlet

to the snow surface depended on the accuracy on the

snow depth determination. The associated error

would be variable, depending on the time passed

from the last visual inspection, and the accuracy of

the interpolation from the SNOTEL record. Further-

more, this error relied on the absolute distance of the

respective inlet to the snow surface. As this error

propagated, its relative value would be larger for

inlets closer to the atmosphere than for inlets nearer

to the soil surface. We estimated the overall range of

the error contributed from uncertainties in the gradi-

ent interval to the surface to be on the order of 10 to

100% in the most extreme cases; the latter for inlets

very close to the snow surface. Temperature mea-

surements inside the snowpack are expected to have a

minor contribution (\5%) to the error estimate, assnowpack air temperatures were measured with a

relative high accuracy and showed little variation

with time and space (Fig. 3). This error may increase

slightly nearer to the surface where temperature

changes were more pronounced than deeper in the

snow.

We also investigated how sampling frequency may

bias the flux calculation. Among previous studies the

frequency of measurements varied widely, ranging

from as often as half-hourly (e.g., Musselman et al.

2005) to as few as twice per winter (e.g., Hubbard et al.

2005). We used a bootstrap randomization without

replacement test to examine the sampling frequency

effects (Supplementary Material, Fig. S2). First, we

calculated a daytime (9 a.m.–5 p.m.) mean to provide a

more realistic comparison to manual sampling proto-

cols. For each sampling frequency the appropriate

number of daytime values (ranging from 5 to

120 days) was randomly selected and a mean calcu-

lated. This process of calculating means was repeated

1,000 times, and the 95% confidence interval was

determined as the 25th and 975th mean (Manly 1997).

The 95% confidence limit for the continuous data was

0.69–0.82 lmol m-2 s-1 in 2007. Monthly samplingresulted in an increase in the 95% confidence interval

ranging from 0.5 to 1.1 lmol m-2 s-1. The 95%confidence interval for weekly sampling (30 samples)

of 0.62–0.88 lmol m-2 s-1 moved close to the resultsfrom our continuous measurements. The results from

this bootstrap analysis meant that a weekly sampling

frequency (i.e. one gradient per week) would give a

mean flux value that was within ±10% of the results

from our continuous measurements of CO2 flux.

Assessment of advection on flux calculations

The observed day-to-day variability in calculated

fluxes and differences in results from different

gradient intervals fully cannot be accounted for even

when combing all of the above considered sampling

and measurement errors and uncertainties, conse-

quently other factors must contribute to the flux

variability. Other research has shown that the CO2efflux from snow-covered soils is sensitive to volu-

metric soil moisture and soil temperature (e.g. Oechel

et al. 1997; Winston et al. 1997; Groffman et al.

2006; Monson et al. 2006). The lack of significant

changes in these variables during DOY -11 to 19

(Fig. 6) suggests that CO2 emissions from the soil

might be reasonably constant over this 30 day period;

it is therefore also unlikely that the variability in the

flux data is caused by changes in the CO2 source

term. We, therefore, conducted further analysis of the

106 Biogeochemistry (2009) 95:95–113

123

potential role that advection may play in the

measured CO2 concentrations and calculated diffu-

sion fluxes in the snowpack.

Snowpack ventilation has been shown to be related

directly to the high frequency pressure gradients that

develop above the surface and inside the snowpack

during windy conditions (Albert and Hawley 2002;

Massman 2006; Massman and Frank 2006). From the

differential pressure data, measured at 1-s resolution,

the 10-min mean values (Fig. 7a), the standard

deviation within each 10-min window (Fig. 7b), and

the amplitude (Fig. 7c) were calculated for the

corresponding time window. All three of these graphs

show strong correlations between these variables,

with the highest degree of correlation seen in the

dependency of the standard deviation of the differ-

ential pressure data on the 10-min mean wind speed

(Fig. 7b). Waddington et al. (1996) described that the

forcing term, the pressure amplitude, has a 2nd order

relationship with wind speed (Aop/ �u2, where A

opis

the amplitude of the mean differential pressure and �u

is the mean wind speed). However, depending on the

topography of the surrounding terrain, a 1st order

relationship between pressure amplitude and wind

speed Aop/ �u

� �may be more appropriate (Massman

and Frank 2006). Our regression analyses, examining

different regression fits, resulted in a best fit (highest

r2) for the 1st order relationship between differential

pressure amplitude and 10-min mean wind speed

(Fig. 7c). These analyses showed that the pressure

amplitude was directly proportional to wind speed.

Thus, it appeared appropriate to use wind speed as the

forcing proxy for assessing advection.

In Figure 8a, concentration gradients from the

60–30 cm interval were plotted against the mean

hourly wind speed during the measurement interval.

With increasing wind speed, the magnitude of the CO2concentration gradient oCCO2=ozj j became progres-sively smaller. The concentration gradient reached

-141 ppm m-1 at the highest recorded winds, while

the gradient for zero wind conditions, as extrapolated

from the 2nd order polynomial regression fit, was

-1,090 ppm m-1. Concentration gradients varied by

a factor of *8 under the wind conditions encounteredduring this experiment. As the concentration gradient

translated proportionally to the final CO2 flux, the flux

results shown in Fig. 8b display a similar range of

dependency, with calculated flux values at the highest

Fig. 7 Relationship between measures of the pressure fluctu-ations, representing the effect of wind pumping, as a function

of absolute 10-min average wind. The differential pressure data

represent a the mean of 1-s data, b the standard deviation of the4,464 measurements within each 10-min interval, and c themean value of the amplitudes that were calculated from the

recorded maximum and minimum values during each minute.

Regression curves shown are the selected best fit results of 1st

and 2nd order regression calculations that were examined. The

blue curves represent the 95% confidence interval of theregression result (Color figure online)

Biogeochemistry (2009) 95:95–113 107

123

winds dropping to a mere 1/8th of values derived under

calm conditions.

Some of our earlier analyses of the diurnal depen-

dency of the CO2 flux had suggested on average 25%

flux increase between early morning and mid afternoon

hours. Figure 9 illustrates this analysis by showing the

mean hourly deviation from the daily mean flux values

(for winters 2006 and 2007) that led to this assumption.

The added wind speed data shed new light on this

discussion. There was an obvious anti-correlation in

the diurnal behavior of winds and calculated flux

values, with higher winds coinciding with lower flux

values and vice versa. Using the amplitudes of winter

2007 data series, the 0.3 m s-1 change in wind speed

corresponded to a -0.05 lmol m-2 s-1 change in thediffusion-calculated CO2 flux. Similarly, for winter

2006, a 0.3 m s-1 change in wind speed yielded a

0.03 lmol m-2 s-1 change in CO2 flux. The winter2007 result agreed with Fig. 10b, where similarly the

slope of the regression function within the linear range

predicted a -0.06 lmol m-2 s-1 change in the diffu-sion-CO2 flux for a 0.3 m s

-1 wind speed increase.

Since results presented in Figs. 8b and 9 were in

qualitative agreement, results from the 30 day period

of analysis shown in Fig. 8b are expected to be

representative for the entire season shown in Fig. 9.

Bowling et al. (2009) illustrated that the transport

of trace gases through the snowpack at the C-1

Fig. 8 a CO2 concentration gradient (oCCO2=oz) and b CO2flux derived from inlets at 30 and 60 cm and wind speed from

DOY -11 to 19 with 2nd order polynomial fit solutions

(y = cx2 ? bx ? a). The blue curves depict the 95%

confidence interval for the fits. The y-intercept, a term, wouldrepresent the CO2 concentration gradient and CO2 flux under

zero wind condition (Color figure online)

Fig. 9 Deviation fromdaily means of wind speed

(left y-axis) and CO2 flux(right y-axis) for winter2006 and 2007. The errorbars are the standard errorsfor each bin of data. The

CO2 fluxes were calculated

from the 60–30 cm

concentration gradient for

both winter 2006 and 2007

108 Biogeochemistry (2009) 95:95–113

123

Ameriflux site on Niwot Ridge was dominated by

diffusion with short-term variability driven by advec-

tion. Furthermore, they showed that the influence of

diffusion was differentially apparent at greater depths.

We evaluated how advection may change the concen-

trations of CO2 between the soil surface and the top of

the snowpack by testing the relationship between CO2concentrations at each inlet height and wind speed

with 2nd order polynomial solutions (y = cx2 ? bx

? a) [Fig. 10]. The regression term a, denoting the

zero-wind speed snowpack CO2 concentration at each

inlet height, linearly increased going from the snow

surface towards the bottom of the snowpack. The term

b demonstrates the ‘‘strength’’ of the wind’s influence

on the CO2 concentration. This value steadily

increased towards the soil surface (going deeper into

the snow), indicating that the wind effect on absolute

CO2 levels was highest at the bottom of the snowpack,

where absolute CO2 concentrations were the highest.

Solutions for c characterized the curvature of the best

fit equation. Here, values increased towards the bottom

of the snowpack, indicating an increasingly higher

sensitivity towards winds deeper in the snow. r2

values, denoting the quality of the regression fit,

increased with increasing depth, showing again that

the wind pumping effect was best described by these

algorithms at the bottom of the snowpack. Lastly, the

95% confidence interval demonstrated how at higher

wind speeds, the uncertainty of CO2 concentration in

the snowpack increases. An important conclusion

from these analyses is that measurements made during

high wind conditions would have increased errors in

calculating CO2 gradients and for flux calculations.

Similar to Bowling et al. (2009), our findings showed

that advection effects at the bottom of the snowpack

were described best by these algorithms.

To demonstrate the bias from wind pumping on

flux results, CO2 fluxes calculated from concentration

data, as obtained during actual wind speed conditions

encountered during DOY -11 to 19, were compared

with fluxes derived from extrapolated gradients for

zero wind speed conditions. These latter values were

derived from the regression equations (intercept

values of the regression solutions presented in

Fig. 10). Fluxes were calculated in both ways for

every sampling interval combination. While results

for individual gradients showed a fair degree of

variability, overall the findings shown in Fig. 11

illustrate that in every case higher flux values were

obtained for the wind-corrected calculation. The

median flux value calculated from the in situ gradient

data of 0.54 lmol m-2 s-1 accounts to 64% of therespective value derived from the wind-corrected

calculation (0.85 lmol m-2 s-1). This findingdefines the possible error that is associated with the

application of Fick’s law under neglect of wind

pumping effects and the resulting underestimation of

flux results.

Summary and conclusions

We have evaluated the DM method for studying

wintertime CO2 fluxes at Niwot Ridge, Colorado. A

particular advantage of this method stems from the

reduced transfer rate (in comparison to ambient air) in

the snowpack, resulting in largely elevated concentra-

tions that build up inside the snow. This condition

causes concentration gradients of gases released from

the subniveal soil reach magnitudes that are much

larger than above the surface, which allowed for their

measurement with relatively simple analytical instru-

ments. Deriving fluxes of these gases requires quan-

titative description of the gas transport in the airspace

of the snowpack. Here, we used the by far most

extensive dataset published to date to examine the

commonly applied Fick’s law of diffusion approach

for computation of fluxes from these data.

Fluxes calculated from all possible gradients from

eight inlet heights were found to generally agree

within a factor of 1.5 with the overall median. Several

factors contribute to variability and uncertainty in

these data, with the error in the snow porosity and

tortuosity variables, which both are indirectly derived

from snow density measurements, being one of the

major contributing factors. This research demon-

strates how these uncertainties are reduced when data

from several gradient heights can be statistically

evaluated and combined for deriving a more repre-

sentative, average flux value.

Fig. 10 Relationship between CO2 concentration measured ateach inlet height above and in the snowpack and wind speed

from DOY -11 to 19 with 2nd order polynomial fit

(y = cx2 ? bx ? a). The blue curve shows the 95% confidenceinterval for the 2nd order fit. Coefficient values printed in red

denote cases that are statistically significant (p \ 0.05). They-intercept, a term, represents the extrapolated CO2 concen-tration under zero wind condition (Color figure online)

c

Biogeochemistry (2009) 95:95–113 109

123

110 Biogeochemistry (2009) 95:95–113

123

Using wind and differential pressure measurements,

we were able to develop the constraints from the

neglect of wind pumping on fluxes derived by the

diffusion approach. Gas concentrations of soil emis-

sions and their snowpack gradients in general declined

with increasing winds, causing a negative bias on

calculated fluxes, with fluxes calculated at the highest

observed winds being less than 13% of those derived

under no-wind conditions. Using an actual 3-week

record from mid-winter, and averaging over all possi-

ble gradient combinations, it was determined that for

conditions at this particular site fluxes calculated by the

diffusion method, neglecting wind-pumping effects,

were 36% lower than wind-corrected calculations.

Acknowledgments This research at Niwot Ridge, Coloradowas funded by the Long-Term Ecological Research grant from

the National Science Foundation (award# NSF DEB9211776).

This work was also supported by NSF grant OPP-0240976. B.

Seok acknowledges the Biosphere-Atmosphere Research

Training (BART) fellowship from the NSF-IGERT program

administrated by the University of Michigan. We thank W.

Massman, US Forest Service, Fort Collins, for fruitful

discussions throughout this study, M. Losleben, University of

Colorado at Boulder, for help with site maintenance and

logistics, and many other University of Colorado colleagues for

support and encouragement in the Niwot Ridge research

projects. Any opinions, findings, and conclusions expressed in

this material are those of the authors and do not necessarily

reflect the views of the National Science Foundation.

Open Access This article is distributed under the terms of theCreative Commons Attribution Noncommercial License which

permits any noncommercial use, distribution, and reproduction

in any medium, provided the original author(s) and source are

credited.

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An automated system for continuous measurements of trace gas fluxes through snow: an evaluation of the gas diffusion method at a subalpine forest site, Niwot Ridge, ColoradoAbstractIntroductionDiffusion model (DM) measurement technique

Materials and methodsStudy siteTrace gas sampling systemAncillary data

ResultsSnow physical propertiesCO2 and H2O vapor concentrations within the snowpackCO2 fluxes

DiscussionPotential sampling effectsDependence of CO2 flux on environmental conditionsUncertainties in flux estimates using the diffusion modelAssessment of advection on flux calculations

Summary and conclusionsAcknowledgmentsReferences

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